Most Local Authorities now publish their Planning Policies, advice & forms on their websites, and you can apply by internet also, but you would need a CAD system to do that - Computer Aided Design, expensive and specialist.
You will be asked to define: use, access, site dimensions, materials... You will need to supply a 'location plan' (OS map), scale drawings showing 'as existing' and 'as proposed' of at least plans, sections, and each elevation including relationship to adjoining properties. Check national requirements on The Planning Portal, but Councils have their own additional demands too. You'll need to pay the Council for handling the application.
You may need to supply other information re environment and landscape protection which may need input of arboriculturalists, BREEAM inspectors, SAP calculators, and write a "Design and Access Statement". Yes you can do it all yourself, but an architect can bear a lot of the grief and collate everything, they get lots of practice!
Then be patient. it will take at least two months. Your application is advertised, immediate neighbours are informed & their views invited. Some applications can be decided by Officers (Council employees), controversial ones will go to Committee (elected politicians) for decision. If you need help with the political angle ask your Local Councillor.
Once over this hurdle it is time to develop the technical detail of your design and submit for Building Regulations Approval. Building Regulations are set out in 'Approved Documents' which refer on to even fatter British Standards & similar. You need to supply details of structure, fire safety, waterproofing, drainage, insulation and ventilation, etc. If you do not meet standards the Council can get your work removed, you also need this approval if say, you have created a room in the roof and want to sell it as an additional bedroom. You may need a structural engineer to identify the support and bracing system and calculate the sizes of load-bearing elements. Environmental standards are now demanding, especially to ensure low energy use, which can require complex calculations.
You will need to comply with the 'Party Wall Act' if relevant, allowing your neighbours time to object, or hopefully formally agree to, your proposed work. Write a letter early on and talk to them.